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Popular >

integral of (2-|x|)

Solution

\int (2 - ∣ x ∣) d x

Solution

2 x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 2 - ∣ x ∣ d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 d x - \int ∣ x ∣ d x

\int 2 d x = 2 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 2 x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= 2 x - \frac{x ∣ x ∣}{2} + C

Popular Examples

integral of ((e^x))/(e^x+3)

\int \frac{( e ^{x} )}{e ^{x} + 3} d x

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\int e^{2 + 2 x} d x

integral of (-9sec(x)tan(x)-7sec^2(x))

\int (- 9 sec (x) tan (x) - 7 sec^{2} (x)) d x

integral of (2x+1)/((x+1)(x-2)^2)

\int \frac{2 x + 1}{( x + 1 ) ( x - 2 ) ^{2}} d x

integral of 12sin(x)cos^3(x)

\int 12 sin (x) cos^{3} (x) d x

Frequently Asked Questions (FAQ)

What is the integral of (2-|x|) ?
The integral of (2-|x|) is 2x-(x|x|)/2+C